Curved Creases

Curved crease folding.<br>Geometry simulation and optimization.

Explore the examples<br>or load your own geometry*

* a polysurface from [untrimmed] ruled surfaces — .3dm format

Constraints

developability

crease

isometry

Shape

fix boundary:

rails

points

anchor Z

folding angle

fairness

Continuity

C1 continuity

angle threshold

Solver

iterations

regression

damping

▶ Optimize

max

&times;

Curved Crease

An interactive tool for designing curved-crease origami.<br>It takes a polysurface of ruled surfaces as input and<br>optimizes the control points so each surface patch<br>becomes developable and satisfies the geometric<br>constraints for valid crease folding between patches.

The optimizer uses a Gauss-Newton solver on B-spline<br>control points, enforcing several residual types:

Developability

Each ruled surface patch must be developable:

(b-a)&middot;n = 0 ruling &perp; normal<br>a'&middot;n = 0 tangent of rail a &perp; normal<br>b'&middot;n = 0 tangent of rail b &perp; normal

Curved Crease

The osculating plane of the crease curve must bisect the dihedral<br>angle between the two surfaces:

a'&middot;(n₁+n₂) = 0 tangent &perp; sum of normals<br>a''&middot;(n₁+n₂) = 0 curvature &perp; sum of normals

Anchor Z

Keeps the height of each control point close to its<br>initial value.

Folding Angle

Soft constrain to keep the initial dihedral angle between adjacent<br>surface patches at each crease.

Fairness

Soft constrain to make every three consecutive<br>control points collinear, producing smoother curves.

C1 Tangent

Enforces tangent continuity at junctions where<br>multiple rails meet.

Regression

Controls how much the geometry changes per step.<br>Higher values stabilize the solver but converge more slowly.

Algorithm Based on

Geometry and Interactive Design of Curved Creases - Klara Mundilova, TU Wien, 2017

Development: Soroush Garivani - soroushgarivani@gmail.com

Logs

Info

Layers

Initial

surfaces

creases

rulings

control points

Optimized

surfaces

creases

rulings

control points

data

crease type

normals

graph

unrolled

creases

rulings

data

crease type

3d

2d

normals

graph

3d

2d

data

crease type

graph

Unroller

stitch

merge

all

2d → 3d

iterations

regression

isometry

merged 2d → 3d

Idle